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The Marine Corps has long been successful in assigning its available personnel inventory to vacant billets. However, by our research, it has not done so while minimizing the assignment costs faced by the Marine Corps when moving a Marine to another permanent duty station. With increased pressure on cost savings due to shrinking budgets, the importance of cost minimizing efforts is becoming more significant. This thesis examines the Marine Corps personnel assignment process and proposes a methodology of optimizing the allocation of Marine Corps personnel that minimizes assignment costs, while taking into account constraints such as military occupational specialty, billet vacancies, duty station preference, and seniority. Optimization is achieved by incorporating an integer programming model into the personnel assignment process. The model is tested by contrasting the results of the actual assignments of a 15 Marine sample with the results of simulated optimization assignments of the same sample. The findings of this thesis show that the proposed methodology is both valid and feasible, and could yield significant monetary savings for the Marine Corps.

Bibliography: leaves 40-42

Bibliography: leaves 40-42

Bibliography: leaves 40-42

Bibliography: leaves 40-42

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by creating a new binary variable for each generated value. Initial experiments show that the extended formulation can have a more compact complete description than the original formulation. We prove that, using this reformulation technique, the facet description decomposes into one ``linking polyhedron'' per block and the ``aggregated polyhedron''. Each of these polyhedra can be analyzed separately. For the case of identical coefficients in a block, we provide a complete description of the linking polyhedron and a polynomial-time separation algorithm. Applied to the knapsack with a fixed number of distinct coefficients, this theorem provides a complete description in an extended space with a polynomial number of variables.

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ADA050244

In many common scenarios, programmers need to implement functionality that is already provided by some third party library. This paper presents a tool called Hunter that facilitates code reuse by finding relevant methods in large code bases and automatically synthesizing any necessary wrapper code. The key technical idea underlying our approach is to use types to both improve search results and guide synthesis. Specifically, our method computes similarity metrics between types and uses this information to solve an integer linear programming (ILP) problem in which the objective is to minimize the cost of synthesis. We have implemented Hunter as an Eclipse plug-in and evaluate it by (a) comparing it against S6, a state-of-the-art code reuse tool, and (b) performing a user study. Our evaluation shows that Hunter compares favorably with S6 and significantly increases programmer productivity.

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of path-width at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded path- width, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification.

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of path-width at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded path- width, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification.

We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite involved. As an alternative to exhaustive enumeration using tailored algorithms we describe the general approach of formulating the problem as an integer linear program.

We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal solution by generating candidate solutions tailored to specific values of the objective function. As a consequence of this strategy, the number of variables in the original ILP problem is systematically reduced without adding any additional constraint to the initial formulation. This is the first of a two-part series on PSAs. In this paper we focus on the resolution of pure integer linear programming (PILP) problems, leaving the treatment of mixed integer linear programming (MILP) formulations to the second part of this series. The proposed algorithm was tested against the IBM ILOG CPLEX [2] optimizer on instances of the 0-1 Multidimensional Knapsack Problem (0-1MKP), showing satisfactory results on instances with a large number of variables.

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.

We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence of linear constraints. The main feature of the latter approach consists in a sophisticated preprocessing phase, leading to a fast enumeration of the branch-and-bound nodes. Moreover, the feasible active set method takes advantage of this preprocessing phase and is well suited for reoptimization. Experimental results for randomly generated instances show that the new approach significantly outperforms the MIQP solver of CPLEX 12.6 for instances with a small number of constraints.

In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed {\em n-fold integer programming problems} are polynomial time solvable. Our proof involves two heavy ingredients discovered recently: the equivalence of linear optimization and so-called directed augmentation, and the stabilization of certain Graver bases. We discuss several applications of our algorithm to multiway transportation problems and to packing problems. One important consequence of our results is a polynomial time algorithm for the $d$-dimensional integer transportation problem for long multiway tables. Another interesting application is a new algorithm for the classical cutting stock problem.

This report develops a hybrid algorithm to solve the binary integer linear programming problem. This problem involves optimizing a linear objective function subject to a set of linear inequalities where, in addition, we require the variables to take on the value 0 or 1. the approach developed is that of implicit enumeration; that is, the set of all possible binary combinations of values for the variables is searched without considering each combination explicitly. This is accomplished by applying a series of tests which when satisfied allow immediate elimination of large subsets of these completions. It is in the choice of tests to be used that this algorithm may be termed a hybrid. Borrowing penalties and pseudocosts as well as binary infeasibility and conditional binary infeasibility tests from previous approaches, the algorithm is built to use each of their strengths. In addition, an existing heuristic procedure is used to generate a good feasible binary point at the outset. Thus, a good initial bound on the optimal function value is available. (Author)

Mixed-Integer Programming has traditionally been restricted to deterministic models. Recent research has opened the door to stochastic optimization models, which are typically dynamic in nature. This project lays the foundation for stochastic dynamic mixed-integer and linear programming (SD-MIP). This project has produced several new ideas in connection with a) convexification of two-stage mixed-integer sets and b) multi-stage (including two-stage) stochastic linear programming. Together a) and b) provide the foundations for SD-MIP problems. From new concepts and algorithms to applications and software, this project has made significant breakthroughs in all aspects. This report provides a synopsis of both theoretical and computational results. As a preview, we mention that currently available deterministic MIP solvers, as powerful as they are known to be, are unable to solve SD-MIP models of modest size within an hour of computing. In contrast, our decomposition approach provides provably optimal solutions within the hour time-limit.

Unmanned aerial vehicles (UAVs) are an essential tool for the battle eld commander in part because they represent an attractive intelligence gathering platform that can quickly identify targets and track movements of individuals within areas of interest. In order to provide meaningful intelligence in near-real time during a mission, it makes sense to operate multiple UAVs with some measure of autonomy to survey the entire area persistently over the mission timeline. This research considers a space where intelligence has identi ed a number of locations and their surroundings that need to be monitored for a period of time. An integer program is formulated and solved to partition this surveillance space into the minimum number of subregions such that these locations fall outside of each partitioned subregion for e cient, persistent surveillance of the locations and their surroundings. Partitioning is followed by a UAV-to-partitioned subspace matching algorithm so that each subregion of the partitioned surveillance space is assigned exactly one UAV. Because the size of the partition is minimized, the number of UAVs used is also minimized.

This paper is proposed to demonstrate the implementation of Mixed-Integer Linear Programming (MILP) for solving the optimal operation of the Integrated Electricity and Natural Gas System (IENGS). The MILP is used to realize an economical and reliable power electricity system based on Dynamic Optimal Power and Gas Flow (DOPGF) considering Take or Pay (TOP) agreements for natural gas. This method is simulated on the integrated 6-bus electricity and 6-node natural gas systems. By using MILP, the best costs for optimal operation of IENGS are obtained in three scenarios. The superiority of the MILP is validated by suppressing the increasing best cost for optimal operation to be below 10%. In the first case, the best cost is $735,405.37 without the TOP agreement. In the second scenario, the best cost ranges from $748,399.30 to $760,320.57 with the TOP agreement implemented in one-by-one generators, which is 1.77% to 3.39% higher than the first scenario. In the third case, the best cost is $791,833.04 with the TOP agreement in all of the generators, which is 7.67% higher than the first scenario. In addition, the MILP can perform the DOPGF for IENGS without violating the problem constraints regarding the load demand fulfillment and power system limitations in both coal-fired and gas-fired generators.  

We present an efficient reduction from the Bounded integer programming (BIP) to the Subspace avoiding problem (SAP) in lattice theory. The reduction has some special properties with some interesting consequences. The first is the new upper time bound for BIP, $poly(\varphi)\cdot n^{n+o(n)}$ (where $n$ and $\varphi$ are the dimension and the input size of the problem, respectively). This is the best bound up to now for BIP. The second consequence is the proof that #SAP, for some norms, is #P-hard under semi-reductions. It follows that the counting version of the Generalized closest vector problem is also #P-hard under semi-reductions. Furthermore, we also show that under some reasonable assumptions, BIP is solvable in probabilistic time $2^{O(n)}$.

Projection from a Business Mathematics course (2005 - 6) by KIT

Projection from a Business Mathematics course (2005 - 6) by KIT

Fundamental Disjunctive Conic Cut (DCC) methodology for Mixed-Integer Conic Linear Optimization (MICO) was developed. To describe the convex hull of the intersection of a convex set E and a linear disjunction is the fundamental problem, and that served as the core of solution techniques for MICO. It was proved that if there exists a cone K that has the same intersection with the boundary of the disjunction as the convex set E, then the convex hull of the disjunction is the intersection of E with K. While uniqueness of a DCC is proved for general MICO, the existence of such a cone is difficult to prove for the general case. Thorough analysis of a parametric family of quadrics allows to prove the existence and uniqueness of a second order cone, when E is the intersection of an affine space and a second order cone. An efficiently computable method was developed for finding that cone, which provided novel and powerful DCCs for Mixed Integer Second Order Cone Optimization (MISOCO), which can be used in branch-and-cut algorithms when solving MISOCO problems. All special and degenerate cases are carefully analyzed and easy to compute criteria are developed to compute a DCC for all cases. Limited, but rigorous computational experiments gave strong indication of the power of the DCCs.

The limited success of exact algorithms for solving integer programming problems has encouraged the development of heuristic procedures for efficiently obtaining solutions that are at least close to optimal. This document presents three heuristic procedures for 0-1 integer programming problems having only inequality constraints. These procedures are based on Hillier's previous heuristic procedures for general integer linear programming. All three were successfully run on problems with up to 500 variables with only modest execution times. The quality of the solutions for these problems were, in general, very good and often were optimal. When the best of the solutions obtained by the three procedures was taken, the final solution was optimal for 24 of 45 randomly generated problems. These procedures can be used for problems that are too large to be computationally feasible for exact algorithms. In addition, they can be useful for smaller problems by quickly providing an advanced starting solution for an exact algorithm.

The report presents a synthesis of the Balasian implicit enumeration approach to integer linear programming with the approach typified by Land and Doig and by Roy, Bertier, and Nghiem. This synthesis results from the use of an imbedded linear program to compute surrogate constraints that are as 'strong' as possible in a sense slightly different from that originally used by Glover. A very simple implicit enumeration algorithm fitted with optional imbedded linear programming machinery was implemented and tested extensively on an IBM 7044 computer. Use of the imbedded linear program dramatically reduced solution time in virtually every case and sufficied to render the tested algorithm superior to the other five implicit enumeration algorithms for which comparable published experience was available. Existing evidence suggests that the present approach should permit the routine solution of practical integer problems involving hundreds of variables.

The paper presents a generalization, called polaroid, of the concept of polar sets. A list of properties satisfied by polaroids is established indicating that the new concept may be fruitfully used in an area of non-convex (called here polar) programming as well as in integer programming, by means of polaroid cuts; this class of new cuts contains the ones defined by Tuy for concave programming (a special case of polar programming) and by Balas for integer programming; it furthermore provides for new degrees of freedom in the construction of algorithms in the above-mentioned areas of mathematical programming.

A primal feasible (all-integer) integer linear programming algorithm has been developed and programmed, together with a related procedure for obtaining a first feasible solution. Once a feasible solution is found, the algorithm maintains feasibility at each stage, in contrast to other algorithms that have been programmed and are currently available. These other algorithms do not achieve feasibility until the optimal solution is reached. The primal feasible algorithm is based on a particular way of applying the cutting planes previously developed by R. E. GOMORY, and on a specific interpretation of their role. The finiteness of convergence has been established for two-dimensional problems but not for the general case; however, there appears to be at least computational convergence in a considerable fraction of the cases. In addition, a Generalized Euclidean Algorithm for finding the greatest common divisor for more than two numbers is defined. The solution of systems of linear diophantine equations is presented in terms of integer linear programming. Some geometric considerations that help to illuminate the workings of the algorithm, are examined.

Contents: Resource Decomposition: A Conceptual Outline; Branching in the Rudimentary Branch-and-Bound Algorithm; Computing Bounds: Single Linking Constraint Case; Computing Bounds: Multiple Linking Constraints Case; Computational Results; and Conclusions, Extensions, and Areas for Future Research.

Detection of an Unmanned Air Vehicle by radar is dependent on many variables including range, altitude, and relative orientation. Given a radar location and appropriate model for the likelihood of detection, a path plan can be created for an Unmanned Air Vehicle which constrains the probability of detection. In this paper such an approach is taken using a linearized detection model. The detection model and the Unmanned Air Vehicle's dynamics are represented as a linear program subject to mixed integer constraints. This mixed integer linear program (MILP) is then solved with commercial software which has been traditionally used by the Operations Research community. This approach searches for all feasible solutions and produces the best path plan based on the user specified parameters.

Integer Programming seminars 1971 - Control Data Corp.

This article is from BMC Systems Biology , volume 8 . Abstract Background: Boolean network (BN) is a mathematical model for genetic network and control of genetic networks has become an important issue owing to their potential application in the field of drug discovery and treatment of intractable diseases. Early researches have focused primarily on the analysis of attractor control for a randomly generated BN. However, one may also consider how anti-cancer drugs act in both normal and cancer cells. Thus, the development of controls for multiple BNs is an important and interesting challenge. Results: In this article, we formulate three novel problems about attractor control for two BNs (i.e., normal cell and cancer cell). The first is about finding a control that can significantly damage cancer cells but has a limited damage to normal cells. The second is about finding a control for normal cells with a guaranteed damaging effect on cancer cells. Finally, we formulate a definition for finding a control for cancer cells with limited damaging effect on normal cells. We propose integer programming-based methods for solving these problems in a unified manner, and we conduct computational experiments to illustrate the efficiency and the effectiveness of our method for our multiple-BN control problems. Conclusions: We present three novel control problems for multiple BNs that are realistic control models for gene regulation networks and adopt an integer programming approach to address these problems. Experimental results indicate that our proposed method is useful and effective for moderate size BNs.

This article is from BMC Systems Biology , volume 8 . Abstract Background: Boolean network (BN) is a mathematical model for genetic network and control of genetic networks has become an important issue owing to their potential application in the field of drug discovery and treatment of intractable diseases. Early researches have focused primarily on the analysis of attractor control for a randomly generated BN. However, one may also consider how anti-cancer drugs act in both normal and cancer cells. Thus, the development of controls for multiple BNs is an important and interesting challenge. Results: In this article, we formulate three novel problems about attractor control for two BNs (i.e., normal cell and cancer cell). The first is about finding a control that can significantly damage cancer cells but has a limited damage to normal cells. The second is about finding a control for normal cells with a guaranteed damaging effect on cancer cells. Finally, we formulate a definition for finding a control for cancer cells with limited damaging effect on normal cells. We propose integer programming-based methods for solving these problems in a unified manner, and we conduct computational experiments to illustrate the efficiency and the effectiveness of our method for our multiple-BN control problems. Conclusions: We present three novel control problems for multiple BNs that are realistic control models for gene regulation networks and adopt an integer programming approach to address these problems. Experimental results indicate that our proposed method is useful and effective for moderate size BNs.

This article is from Bioinformatics , volume 28 . Abstract Motivation: The prediction of RNA 3D structures from its sequence only is a milestone to RNA function analysis and prediction. In recent years, many methods addressed this challenge, ranging from cycle decomposition and fragment assembly to molecular dynamics simulations. However, their predictions remain fragile and limited to small RNAs. To expand the range and accuracy of these techniques, we need to develop algorithms that will enable to use all the structural information available. In particular, the energetic contribution of secondary structure interactions is now well documented, but the quantification of non-canonical interactions—those shaping the tertiary structure—is poorly understood. Nonetheless, even if a complete RNA tertiary structure energy model is currently unavailable, we now have catalogues of local 3D structural motifs including non-canonical base pairings. A practical objective is thus to develop techniques enabling us to use this knowledge for robust RNA tertiary structure predictors.Results: In this work, we introduce RNA-MoIP, a program that benefits from the progresses made over the last 30 years in the field of RNA secondary structure prediction and expands these methods to incorporate the novel local motif information available in databases. Using an integer programming framework, our method refines predicted secondary structures (i.e. removes incorrect canonical base pairs) to accommodate the insertion of RNA 3D motifs (i.e. hairpins, internal loops and k-way junctions). Then, we use predictions as templates to generate complete 3D structures with the MC-Sym program. We benchmarked RNA-MoIP on a set of 9 RNAs with sizes varying from 53 to 128 nucleotides. We show that our approach (i) improves the accuracy of canonical base pair predictions; (ii) identifies the best secondary structures in a pool of suboptimal structures; and (iii) predicts accurate 3D structures of large RNA molecules.Availability:RNA-MoIP is publicly available at: http://csb.cs.mcgill.ca/RNAMoIP.Contact:[email protected]

We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer features such as anytime optimization and parallel search that are highly relevant for query optimization. We present a MILP formulation for searching left-deep query plans. We use sets of binary variables to represent join operands and intermediate results, operator implementation choices or the presence of interesting orders. Linear constraints restrict value assignments to the ones representing valid query plans. We approximate the cost of scan and join operations via linear functions, allowing to increase approximation precision up to arbitrary degrees. Our experimental results are encouraging: we are able to find optimal plans for joins between 60 tables; a query size that is beyond the capabilities of prior exhaustive query optimization methods.

We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer features such as anytime optimization and parallel search that are highly relevant for query optimization. We present a MILP formulation for searching left-deep query plans. We use sets of binary variables to represent join operands and intermediate results, operator implementation choices or the presence of interesting orders. Linear constraints restrict value assignments to the ones representing valid query plans. We approximate the cost of scan and join operations via linear functions, allowing to increase approximation precision up to arbitrary degrees. Our experimental results are encouraging: we are able to find optimal plans for joins between 60 tables; a query size that is beyond the capabilities of prior exhaustive query optimization methods.

This research develops a mixed integer linear programming (MILP) model that considers simultaneously both the traditional reservoir rule curves and the hedging rules to manage and operate a multipurpose, multireservoir system. During normal periods of operation, when inflows are plentiful, this optimization model efficiently distributes the available stored water from different reservoirs to meet the planned demands imposed by competing users. However, during periods of drought, or when anticipating a drought, the planned demands cannot be fully met, and a water shortage occurs. By considering the hedging rules along with the rule curves, guidelines are provided for reservoir releases. To minimize the impact of drought, the hedging rules effectively reduce the ongoing water supply to balance with the target storage requirement. The MILP model is applied to a multireservoir system in the southern region of Taiwan, where the results obtained demonstrate the applicability and utility of the model. Read More: http://ascelibrary.org/action/showAbstract?page=86&volume=129&issue=2&journalCode=jwrmd5

Inspired by a paper of R. W. Rosenthal, we investigate generalized Nash-equilibria of integer programming games. We show that generalized Nash-equilibria always exist and are related to an optimal solution of a so-called N-fold integer program. This link allows us to establish some polynomial time complexity results about solving this optimization problem and its inverse counter-part.

Lecture from a Business Mathematics course (2005 - 6) by KIT

Lecture from a Business Mathematics course (2005 - 6) by KIT

A quadratic program (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This is done via the reformulation of QP as a linear complementary problem, and the use of binary variables together with some fundamental results on the solution of perturbed linear systems, to model the complementary constraints. Reformulating non-convex QPs as MILPs provides an advantageous way to obtain global solutions as it allows to use current state-of-the-art MILP solvers. To illustrate, we compare the performance of our solution approach with the current benchmark global QP solver quadprogBB on a large variety of QP test instances. The MATLAB code, called quadprogIP, and the instances used to perform these numerical experiments are publicly available at https://github.com/xiawei918/quadprogIP.

A quadratic program (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This is done via the reformulation of QP as a linear complementary problem, and the use of binary variables together with some fundamental results on the solution of perturbed linear systems, to model the complementary constraints. Reformulating non-convex QPs as MILPs provides an advantageous way to obtain global solutions as it allows to use current state-of-the-art MILP solvers. To illustrate, we compare the performance of our solution approach with the current benchmark global QP solver quadprogBB on a large variety of QP test instances. The MATLAB code, called quadprogIP, and the instances used to perform these numerical experiments are publicly available at https://github.com/xiawei918/quadprogIP.

In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings. The MCSP seeks a minimum cardinality partitioning of one string into non-overlapping substrings that is also a valid partitioning for the second string. This problem has applications in bioinformatics e.g. in analyzing related DNA or protein sequences. For strings with lengths less than about 1000 letters, a previously published integer linear programming (ILP) formulation yields, when solved with a state-of-the-art solver such as CPLEX, satisfactory results. In this work, we propose a new, alternative ILP model that is compared to the former one. While a polyhedral study shows the linear programming relaxations of the two models to be equally strong, a comprehensive experimental comparison using real-world as well as artificially created benchmark instances indicates substantial computational advantages of the new formulation.

We give a worst case analysis for two greedy heuristics for the integer programming problem minimize cx, Ax or = b, O or = x or = u, x integer, where the entries A, b, and c are all non-negative. The first heuristic is for the case where the entries in A and b are integral, the second only assumes the rows are scaled so that the smallest nonzero entry is at least 1. In both cases we compare the ratio of the value of the greedy solution to that of the integer optimal. The error bound grows logarithmically in the maximum column sum of A for both heuristics. (Author)

The computer code SDA to be described in this report solves the staircase integer linear programming problem. This formulation arises in multiplant production allocation problems, multisector economic planning models, and multitime period production and inventory problems. The solution method used by the program SDA relies upon decomposition of the problem (SP) into smaller subproblems (St), each of which can then be efficiently solved by an LP-based branch-and-bound routine. (Author)

The computer code SDA to be described in this report solves the staircase integer linear programming problem. This formulation arises in multiplant production allocation problems, multisector economic planning models, and multitime period production and inventory problems. The solution method used by the program SDA relies upon decomposition of the problem (SP) into smaller subproblems (St), each of which can then be efficiently solved by an LP-based branch-and-bound routine. (Author)

N-fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer programming. The fastest algorithm for $n$-fold integer programming predating the present article runs in time $O(n^{g(A)}L)$ with $L$ the binary length of the numerical part of the input and $g(A)$ the so-called Graver complexity of the bimatrix $A$ defining the system. In this article we provide a drastic improvement and establish an algorithm which runs in time $O(n^3 L)$ having cubic dependency on $n$ regardless of the bimatrix $A$. Our algorithm can be extended to separable convex piecewise affine objectives as well, and also to systems defined by bimatrices with variable entries. Moreover, it can be used to define a hierarchy of approximations for any integer programming problem.

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a novel mixed integer programming formulation to construct optimal decision trees of specified size. We take special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of such a feature) at each node. We show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are easily tractable with modern solvers.

Integer Programming Problems (IPPs) play a critical role in solving real-world optimization scenarios where decision variables must be integers, such as in scheduling, logistics, and resource allocation. Traditional methods like Branch and Bound and Cutting Plane techniques have been widely used for solving such problems. In 2003, Bari and Ahmad introduced the NAZ-cut method, a straightforward and computationally efficient approach to solving IPPs by systematically reducing the feasible solution space through the addition of specific constraints. This paper presents an enhanced NAZ-cut framework for solving IPPs, particularly in the context of Fermatean fuzzy environments, where uncertainty in parameters is modeled using Fermatean fuzzy sets. A new approach is proposed to minimize computational effort by excluding specific integer candidate solutions based on a well-defined criterion. A supporting theorem is provided to justify this exclusion, ensuring that only feasible and potentially optimal points are considered. The method is demonstrated through a numerical example, highlighting the effectiveness of the proposed strategy in simplifying the search process and improving computational efficiency.

LibriVox volunteers bring you fifteen different readings of <i>Mother Night</i>, by James Weldon Johnson. This weekly poetry project (for the week of Feb 26, 2006) was selected to celebrate Black History Month.<br>(Summary by Annie Coleman)

In celebration of <a href="http://en.wikipedia.org/wiki/Juneteenth">Juneteenth</a>, LibriVox volunteers bring you five different versions of <em>O Southland!</em>, by James Weldon Johnson. This was the weekly poetry project for 18 June 2006.<br />(Summary by Annie Coleman)

3Song My Paddle Sings

By E. Pauline Johnson

LibriVox’s weekly poetry project for the week of February 5, 2006 offers fourteen versions of "The Song My Paddle Sings" from the collection <i>Flint and Feather</i> by E. Pauline Johnson.<br /><br /> E. Pauline Johnson, also known as Tekahionwake, was born to the Mohawk Chief G.H.M. Johnson (Onwanonsyshon), and his wife, Emily S. Howells, a lady of pure English parentage. Pauline, born and raised in Canada, was a great reader and began writing poetry as a child. She died in 1913 after having poetry published in periodicals in several countries and collections of her work published in book form. (Summary adapted from the "Biographical Sketch" included in the Gutenberg text.)

4Plan and Preface to a Dictionary of the English Language

By Samuel Johnson

The published dictionary was a huge book: with pages nearly 1½ feet tall and 20 inches wide, it contained 42,773 words; it also sold for the huge price of £4/10s. ($400?). It would be years before "Johnson's Dictionary", as it came to be known, would ever turn a profit; authors' royalties being unknown at that time, Johnson, once his contract to deliver the book was fulfilled, received no further monies connected to the book.<br><br> Johnson, once again a freelance writer, albeit now a famous one, faced a grim hand-to-mouth existence; however, in July 1762 the twenty-four year old King George III granted Johnson an annual pension of £300. While not making Johnson rich, it allowed him a modest yet comfortable independence for the remaining thirty years of his life. (Summary from Wikipedia).

A book of simple receipts for little folk with important cooking rules in rhyme together with handy lists of the materials and utensils needed for the preparation of each dish. (Summary from the text)

6Rasselas, Prince of Abyssinia

By Samuel Johnson

In this enchanting fable (subtitled The Choice of Life), Rasselas and his retinue burrow their way out of the totalitarian paradise of the Happy Valley in search of that triad of eighteenth-century aspiration - life, liberty and happiness.<br><br/>According to that quirky authority, James Boswell, Johnson penned his only work of prose fiction in a handful of days to cover the cost of his mother's funeral. The stylistic elegance of the book and its wide-ranging philosophical concerns give no hint of haste or superficiality. <br><br/> Among other still burning issues Johnson's characters pursue questions of education, colonialism, the nature of the soul and even climate alteration. <br> Johnson's profoundest concern, however, is with the alternating attractions of solitude and social participation, seen not only as the ultimate life-choice but as the arena in which are played out the deepest fears of the individual: "Of the uncertainties of our present state, the most dreadful and alarming is the uncertain continuance of Reason.” (Summary by Martin Geeson)

A General History of the Robberies and Murders of the most notorious Pyrates is a 1724 book containing biographies of contemporary pirates. It's author uses the name Captain Charles Johnson, generally considered a pseudonym.<br /><br /> The real identity of the author was thought by some scholars to be Daniel Defoe, although this has since been disputed. The publisher Nathaniel Mist or somebody working for him are other suggested authors.<br /><br /> In the first volume, "Johnson" sticks fairly close to the available sources, though he embellishes the stories somewhat. Nevertheless, the book was influential in shaping popular notions of piracy and provided the standard account of the lives of many individuals still famous in the 21st century.(Summary by Wikipedia)

A year in the life of a New England farm boy at the end of the 19th century (Introduction by LC)

9Train Dogs

By E. Pauline Johnson

LibriVox volunteers bring you 18 recordings of The Train Dogs by E. Pauline Johnson. This was the Weekly Poetry project for February 6th, 2011.<br><br>Emily Pauline Johnson (Mohawk: Tekahionwake –pronounced: dageh-eeon-wageh, literally: 'double-life')(10 March 1861 – 7 March 1913), commonly known as E. Pauline Johnson or just Pauline Johnson, was a Canadian writer and performer popular in the late 19th century. Johnson was notable for her poems and performances that celebrated her First Nations heritage; she also had half English ancestry. One such poem is the frequently anthologized "The Song My Paddle Sings". Her poetry was published in Canada, the United States and Great Britain. Johnson was one of a generation of widely read writers who began to define a Canadian literature.

10Sunset in the Tropics

By James Weldon Johnson

LibriVox volunteers bring you 14 recordings of "Sunset in the Tropics." This is the Weekly Poetry for the week of August 10, 2014.<br><br>The author of this poem, James Weldon Johnson, served as U. S. Consul to Venezuela and Nicaragua, was an early leader in the NAACP and contributed to the Harlem Renaissance of the 1920s. He had a broad appreciation for black artists, musicians and writers, and worked to heighten awareness of their creativity. (from Wikipedia)

A shot penetrates the still night air and one of Galton's leading citizens is a victim of a desperate killer's gun. Murder becomes entangled with politics and it takes a parish priest to discover "whodunit" in this thriller by a husband and wife novelist team. (Summary taken from original jacket blurb.)

County Prosecutor Wally Brighton was found shot to death one evening, a broken rosary in one hand and a .32 automatic inches away from the other. Was it murder or suicide? It takes two sharp-eyed reporters, who combine romance with amateur sleuthing, to find the surprising solution to this baffling and thrilling murder mystery. (Summary from an original jacket)

13Cry From An Indian Wife

By E. Pauline Johnson

LibriVox volunteers bring you 13 recordings of A Cry From an Indian Wife by E. Pauline Johnson,. This was the Fortnightly Poetry project for January 29, 2012.<br><br>In 1892 the opportunity of a lifetime came to this young versifier, when Frank Yeigh, the president of the Young Liberals' Club, of Toronto, conceived the idea of having an evening of Canadian literature, at which all available Canadian authors should be guests and read from their own works.<br><br>Among the authors present on this occasion was Pauline Johnson, who contributed to the programme one of her compositions, entitled "A Cry from an Indian Wife"; and when she recited without text this much-discussed poem, which shows the Indian's side of the North-West Rebellion, she was greeted with tremendous applause from an audience which represented the best of Toronto's art, literature and culture. She was the only one on the programme who received an encore, and to this she replied with one of her favourite canoeing poems.<br><br>The following morning the entire press of Toronto asked why this young writer was not on the platform as a professional reader; while two of the dailies even contained editorials on the subject, inquiring why she had never published a volume of her poems, and insisted so strongly that the public should hear more of her, that Mr. Frank Yeigh arranged for her to give an entire evening in Association Hall within two weeks from the date of her first appearance. It was for this first recital that she wrote the poem by which she is best known, "The Song my Paddle Sings."<br>( Summary from the Biographical Sketch included in Flint And Feather, collected verse by E. Pauline Johnson )

14Indian Corn Planter

By E. Pauline Johnson

LibriVox volunteers bring you 13 recordings of The Indian Corn Planter by E. Pauline Johnson. This was the Weekly Poetry project for April 29, 2012.<br><br><i>"But in the writings of one poet alone I came upon a new note—the note of the Red Man's Canada. This was the poet that most interested me—Pauline Johnson. I quoted her lovely canoe song "In the Shadows," which will be found in this volume. I at once sat down and wrote a long article, which could have been ten times as long, upon a subject so suggestive as that of Canadian poetry."</i> (From the Introduction to Flint and Feather, Collected Verse BY E. Pauline Johnson; written by Theodore Watts-Dunton, The Pines, Putney Hill. 20th August, 1913.

15Fire - Flowers

By E. Pauline Johnson

LibriVox volunteers bring you 17 recordings of Fire - Flowers by E. Pauline Johnson. This was the Fortnightly Poetry project for August 18, 2013.<br><br>Fire-Flowers is taken from the book, Flint and Feather: Collected Verse by E. Pauline Johnson. (Summary by David Lawrence)

16Word of an Engineer

By James Weldon Johnson

James Weldon Johnson was an American author, educator, lawyer, diplomat, songwriter, and civil rights activist. Johnson is best remembered for his leadership within the National Association for the Advancement of Colored People (NAACP), where he started working in 1917, being chosen as the first black executive secretary of the organization, effectively the operating officer. He was first known for his writing, which includes poems, novels, and anthologies collecting both poems and spirituals of black culture. (Summary from Wikipedia)

17Morning, Noon and Night

By James Weldon Johnson

LibriVox volunteers bring you 14 readings of Morning, Noon and Night by James Weldon Johnson. This was the weekly poetry project for the week of September 14th, 2014.<br /><br />James Weldon Johnson served as U. S. Consul to Venezuela and Nicaragua, was an early leader in the NAACP and contributed to the Harlem Renaissance of the 1920s. He had a broad appreciation for black artists, musicians and writers, and worked to heighten awareness of their creativity. (from Wikipedia)

This is a volume of selected essays by "the great master of reason" Samuel Johnson. The most famous exerpts from The Rambler, The Adventurer and The Idler are included, covering a vast range of topics. - Summary by Carolin

19Deep In The Quiet Wood

By James Weldon Johnson

James Weldon Johnson was an American author, educator, lawyer, diplomat, songwriter, and civil rights activist. Johnson is best remembered for his leadership of the National Association for the Advancement of Colored People (NAACP), where he started working in 1917. In 1920 he was the first black to be chosen as executive secretary of the organization, effectively the operating officer. He served in that position from 1920 to 1930. Johnson established his reputation as a writer, and was known during the Harlem Renaissance for his poems, novels, and anthologies collecting both poems and spirituals of black culture.

20Sonnet (From the Spanish of Plácido)

By James Weldon Johnson

James Weldon Johnson was an American author, educator, lawyer, diplomat, songwriter, and civil rights activist. Johnson is best remembered for his leadership of the National Association for the Advancement of Colored People (NAACP), where he started working in 1917. In 1920 he was the first black to be chosen as executive secretary of the organization, effectively the operating officer. - Summary by Wikipedia

21Autobiography of an Ex-Colored Man (version 2)

By James Weldon Johnson

The story of a biracial man living in the deep south after the reconstruction era. He is young and talented. Yet, in order for him to avoid stigma, he has to pass as white. But would his sense of belonging and solidarity to the black community of the time catch up with him at the end? "It is very likely that the Negroes of the United States have a fairly correct idea of what the white people of the country think of them, for that opinion has for a long time been and is still being constantly stated; but they are themselves more or less a sphinx to the whites. It is curiously interesting and even vitally important to know what are the thoughts of ten millions of them concerning the people among whom they live. In these pages it is as though a veil had been drawn aside: the reader is given a view of the inner life of the Negro in America, is initiated into the "freemasonry," as it were, of the race. These pages also reveal the unsuspected fact that prejudice against the Negro is exerting a pressure which, in New York and other large cities where the opportunity is open, is actually and constantly forcing an unascertainable number of fair-complexioned colored people over into the white race. In this book the reader is given a glimpse behind the scenes of this race-drama which is being here enacted,—he is taken upon an elevation where he can catch a bird's-eye view of the conflict which is being waged." (from the preface by the publisher and Stav Nisser.)

22Autobiography of an Ex-Colored Man

By James Weldon Johnson

Johnson's only novel, <i>The Autobiography of an Ex-Colored Man</i>, was originally published anonymously in 1912. It is a fictional novel written as a memoir of an unnamed biracial narrator who grew up in the South during the Reconstruction and post-Reconstruction eras. It is a story in which the narrator relates how as a young boy he initially assumed that he was white, and how his notions of racial identity were suddenly turned upside down one day—how from that moment on he was inclined to view himself and the world about him from the perspective of blackness. The novel received very little notoriety until Johnson republished it in 1927, this time taking full credit as its author. - Summary by James K. White

23Camper

By E. Pauline Johnson

It is eminently fitting that this daughter of Nature should have been laid to rest in no urban cemetery. According to her own request she was buried in Stanley Park, Vancouver's beautiful heritage of the forest primeval. A simple stone surrounded by rustic palings marks her grave and on this stone is carved the one word "Pauline." There she lies among ferns and wild flowers a short distance from Siwash Rock, the story of which she has recorded in the legends of her race. In time to come a pathway to her grave will be worn by lovers of Canadian poetry who will regard it as one of the most romantic of our literary shrines. (from the Biographical Sketch in Flint and Feather: Collected Verse by E. Pauline Johnson)

24Homing Bee

By E. Pauline Johnson

It is eminently fitting that this daughter of Nature should have been laid to rest in no urban cemetery. According to her own request she was buried in Stanley Park, Vancouver's beautiful heritage of the forest primeval. A simple stone surrounded by rustic palings marks her grave and on this stone is carved the one word "Pauline." There she lies among ferns and wild flowers a short distance from Siwash Rock, the story of which she has recorded in the legends of her race. In time to come a pathway to her grave will be worn by lovers of Canadian poetry who will regard it as one of the most romantic of our literary shrines. (from the Biographical Sketch in the Flint and Feather collection)

25Erie Waters

By E. Pauline Johnson

"Her death is not only a great loss to those who knew and loved her: it is a great loss to Canadian literature and to the Canadian nation. I must think that she will hold a memorable place among poets in virtue of her descent and also in virtue of the work she has left behind, small as the quantity of that work is. I believe that Canada will, in future times, cherish her memory more and more, for of all Canadian poets she was the most distinctly a daughter of the soil, inasmuch as she inherited the blood of the great primeval race now so rapidly vanishing, and of the greater race that has supplanted it." (Theodore Watts-Dunton, from the Introduction to Flint and Feather)

26Famous Assassinations Of History

By Francis Johnson

It has been the object of the writer to make each of these “famous assassinations” the central scene of a picture in which the political, religious, or national features of the epoch in which the assassination occurred are portrayed with historical fidelity and strict impartiality…. Only those assassinations have been included which either had an important and political bearing on the world, or on the nation immediately affected, or which left a profound, and, it would seem, indelible impression on the imagination of contemporaries and posterity. - Summary by Book Preface

Wild animals play a big role in many fairy tales, and foxes are some of the best-represented animals in folklore. In this volume, Clifton Johnson has collected stories about foxes from all over the world, adapted for children as bedtime fairy tales. - Summary by Carolin